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Suppose that you have 10 identical components in a machine, and that the lifetime of each component is independent of all the others. Assume that each component's lifetime has an exponential distribution with the mean lifetime of w hours.

You start the machine, and leave it operating alone for 24 hours. Upon return you notice that 2 of 10 components have failed.

a. What is the probability of exactly 2 out of 10 components failing within 24 hours?

b. Write down the likelihood function as a function of w.

c. What value of w maximizes the likelihood function? (Find the maximum likelihood estimate of w.)

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